1. Technical Field
The present invention relates generally to a multivariate digital camera device and method for generating pictures of datasets comprised of points in hyperspace using an input device, a computer processor, and an output device to produce 2D and 3D representations of the datasets.
2. Description of the Related Art
Research studies and experiments in various scientific disciplines require the analysis of datasets comprised of points in hyperspace. The term “hyperspace” is defined herein as the mathematical construct of four or more dimensional space in contrast to a two- and three-dimensional space, referred to herein as 2D and 3D, respectively. Such datasets to be analyzed consist of points defined by four or more variables, also referred to herein as multivariate data, which can be denoted as (x, y, z, . . . , n) where x represents the first variable, y represents the second variable, z represents the third variable, and so forth up to a variable denoted here as n. The challenge in analyzing such datasets is that humans can only visualize 2D and 3D objects. With the exception of using time as the fourth dimension, humans cannot visualize multivariate datasets without some form of dimensional reduction, projection, mapping, or illustration tool that reduces the multivariate data to either 2D or 3D form.
Scientists and mathematicians have developed methods to help visualize an object or collection of points in hyperspace by reducing the dataset to a 2D or 3D rendering. Such methods can be referred to generally as multivariate data analysis (MVA). Conventional MVA, also referred to herein as principal component analysis (PCA), finds a first principal component or factor vector in the hyperspace dispersion of points. This procedure uses all the points in the dataset and a line is drawn through hyperspace. All points are projected onto that line by perpendicular lines that cut or intersect with the introduced vector. The vector is rotated such that the intersections of the projected points onto a principal component vector create the widest dispersion of their projections onto the principal component vector. That vector is named the first principal component or first factor. The next or second factor or principal component by definition is perpendicular to the first. As with the first vector, points are projected onto this second line until the orientation of the line or vector is such that the intersection of the projected points onto the vector creates the widest dispersion of projections on the principal component vector. That vector is named the second principal component or second factor. This continues for the third factor and higher factors until all factors are obtained for the multivariate data. That is, if the multivariate data are in or representative of ten dimensions (n=10), then the process is continued until ten factors are obtained.
The prior art PCA method described above relies on obtaining and using a depth parameter for visualization of a hyperspace object in 2D or 3D. Unlike a multivariate camera, the relative distances and angles of each point in a hyperspace object are not measured and retained. Therefore all points of the hyperspace object are not individually imaged into or onto a 2D or 3D format for human visualization. The term “format” and “surface” may be used interchangeably in this context.
Another type of related prior art method involves use of a dendrogram. A dendrogram is a tree diagram that can be used to illustrate the arrangement of hierarchical clustering. While providing useful information about the hyperspace data, this prior art method uses the Euclidean distances between points in hyperspace in order to derive the hierarchical clustering to be illustrated. The angles formed by the lines connecting points in hyperspace are not used to guide and orient distance projections, so any information or insight to be gained by such data are not present in the resulting dendrogram.
Accordingly, there is a need for a multivariate digital camera device and method that utilizes both the distances data as well as the angles data from each point in the dataset to generate 2D and 3D pictures of hyperspace objects.